Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1424 | C2 | semidirect |
| 2. C2×#19151835 | C2 | semidirect |
| 3. C2×#19151398 | C2 | semidirect |
| 4. C2×#19151377 | C2 | semidirect |
| 5. C89×#1380 | C2 | semidirect |
| 27. C2×D712 | D4 | semidirect |
| 43. C2×C16×C89 | D4 | semidirect |
| 45. #107×C89 | D4 | semidirect |
| 94. C22×D89 | D16 | semidirect |
| 150. #1380 | D89 | semidirect |
| 151. C89 | #13304 | semidirect |
| 188. C2×C16 | D356 | semidirect |
| 190. #107 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151835 | 2 |
| C2×#19151398 | 2 |
| C2×#19151377 | 2 |
| C89×#1380 | 2 |
| #13304 | 89 |